Reeb 1-curve conjecture for closed exact lcs four-manifolds

Let $(M,\lambda,\alpha)$ be a closed exact locally conformally symplectic manifold of dimension $4$ satisfying the Reeb condition. A Reeb 1-curve is the type of Reeb curve considered in the paper.

Reeb 1-curve conjecture. The manifold $M$ has a Reeb 1-curve.

The claim extends the preceding existence results for Reeb 1-curves, including the corresponding result for closed exact locally conformally symplectic surfaces. Its resolution is not indicated in the source.